Case 44: Water -Ten Pipe Network with Back Pressure Valve(BPV)
Reference: Hydraulics of Pipeline Systems, 2000, CRC Press LLC, Bruce E. Larock, Rowland W. Jeppson, Gary Z. Watters, Page 70, Example figure 4.10
Pipe Flow Expert File: Case_44_Water_Ten_Pipe_Network_With_Back_Pressure_Valve(BPV).pfe
Problem Description:
A network of 10 interconnected pipes delivers water from three reservoirs to outlet demands at six pipework junctions. The network includes a pump.
The pressure at a node where two pipes join is controlled by a back pressure valve set to 12.2583 barg. The elevation of the BPV node is 70 ft.
Calculate the flow rate in each individual pipe and the pump head added to the system.
Fluid Data: Water at 10° C (assumed).
Result Comparison:
|
Data Item |
Published data |
Pipe Flow Expert |
|
P1 Flow rate (m³/s) |
0.102 |
0.1024 |
|
P2 Flow rate (m³/s) |
0.004 |
0.0036 |
|
P3 Flow rate (m³/s) |
0.091 |
0.0910 |
|
P4 Flow rate (m³/s) |
0.006 |
0.0057 |
|
P5 Flow rate (m³/s) |
0.009 |
0.0093 |
|
P6 Flow rate (m³/s) |
0.015 |
0.0153 |
|
P7 Flow rate (m³/s) |
0.035 |
0.0353 |
|
P8 Flow rate (m³/s) |
0.065 |
0.0653 |
|
P9 Flow rate (m³/s) |
0.014 |
0.0140 |
|
P10 Flow rate (m³/s) |
0.006 (same as P4) |
0.0057 |
|
Pump - head added |
34.88 m fluid |
34.879 m fluid |
|
HGL at BPV Node N10 |
195.00 m |
195.000 m |
|
Pressure at Node N2 (kPa) |
580.7 (Node 1 in text) |
581.468 |
|
Pressure at Node N4 (kPa) |
539.2 (Node 2 in text) |
539.595 |
|
Pressure at Node N5 (kPa) |
579.0 (Node 3 in text) |
578.62 |
|
Pressure at Node N6 (kPa) |
695.6 (Node 4 in text) |
695.622 |
|
Pressure at Node N6 (kPa) |
555.3 (Node 5 in text) |
555.355 |
|
Pressure at Node N6 (kPa) |
683.8 (Node 6 in text) |
684.158 |
Commentary:
The published data and the calculated results compare well.
Pipe Flow Expert correctly identified that pipe 5 and pipe 6 were drawn with the wrong flow direction in the design schematic. These pipes were automatically reversed and the flows were reported as positive values.
The reference text schematic shows the elevation of node N2 as 150 m however the input reference table correctly identifies the elevation as 140.0 m.